The present invention relates to migration of seismic reflections performed in a high-speed digital computer, and more particularly to modeling and imaging seismic wave propagation in the earth using Hale-McClellan wave propagation computations.
For many years seismic exploration for oil and gas has involved the use of a source of seismic energy and its reception by an array of seismic detectors, generally referred to as geophones. When used on land, the source of seismic energy can be a high explosive charge electrically detonated in a borehole located at a selected point on a terrain or another energy source having capacity for delivering a series of impacts or mechanical vibrations to the earth""s surface. Offshore, air gun sources and hydrophone receivers are commonly used. The acoustic waves generated in the earth by these sources are transmitted back from strata boundaries and reach the surface of the earth at varying lengths of time, depending on the distance and the characteristics of the subsurface the waves traveled. These returning waves are detected by geophones, which function to transduce such acoustic waves into representative electrical signals. In use, geophones are generally laid out along a line to form a series of observation stations within a desired locality, the source injects acoustic signals into the earth, and the detected signals are recorded for later processing using digital computers where the data are generally quantized as digital sample points such that each sample point may be operated on individually. Accordingly, seismic field records are reduced to vertical and horizontal cross sections which approximate subsurface features. The geophone array is then moved along the line to a new positions and the process repeated to provide a seismic survey. More recently seismic surveys involve geophones and sources laid out in generally rectangular grids covering an area of interest so as to expand areal coverage and enable construction of three dimensional (3D) views of reflector positions over wide areas.
As oil and gas production from known reservoirs and producing provinces declines, explorationists seek new areas in which to find hydrocarbons. Many of the new areas under exploration contain complex geological structures that are difficult to image with 2D techniques. Accordingly, 3D seismic processing has come into common use for mapping subterranean structures associated with oil and gas accumulations. Geophysicists, however, are well aware that a 2D seismic record section or 3D view is not a true reflectivity from the earth, but is instead a transformation of the earth""s reflectivity into a plane where each recorded event is located vertically beneath the source/receiver midpoint. Steep dip, curved surfaces, buried foci, faults and other discontinuities in subterranean structure each contribute their unique characteristics to the seismic record and, in complexly faulted and folded areas, make interpretation of the geological layering from the seismic record extremely difficult.
Migration is the inverse transformation that carries the plane recorded events into a true 3D reflectivity of the earth, thereby placing reflections from dipping beds in their correct location and collapsing diffractions. Of the various available migration methods, wave equation migration is considered to be superior because it is based on accurate propagation of seismic waves through complex models of the earth. Seismic migration consists of two steps; first, wave extrapolation and, second, imagining. Downward extrapolation results in a wave field that is an approximation to the one that would have been recorded if both sources and recorders had been located a depth z. Wave extrapolation complexity depends largely on the migration velocity function. Whereas imaging represents little problem, the wave extrapolation can be quite complex where there are lateral velocity variations. These difficulties are particularly egregious in 3D depth migration Accordingly, most migration schemes concentrate on solving the difficulties associated with wave extrapolation.
Several different numerical techniques have been used to attempt to develop an accurate 3D prestack depth migration. Generally, both implicit depth extrapolation and explicit depth extrapolation have been used.
Implicit depth extrapolation methods involve solving a linear system of coupled equations. Stability has been one of the most compelling reasons for the use of implicit methods for seismic wavefield extrapolation. However, attempts to use implicit methods have been hindered by the fact that commonly used methods, such as finite-difference migration methods, cannot be extended easily from 2D to 3D. Splitting the depth extrapolation process to extrapolate alternately along the inline (x) and crossline (y) directions is the most practical way to extend implicit extrapolation methods from 2D to 3D. However, splitting results in errors depending significantly on reflector dip and azimuth. Corrections for these errors increase both the computational cost and complexity of implicit depth extrapolation methods.
More recent methods, such as reverse-time migration, may be extended from 2D to 3D relatively easily but are relatively expensive, due to the large number of computations and the large amount of computer memory required.
Explicit methods for seismic wavefield extrapolation are attractive because they require relatively less computations and computer memory. However, explicit methods tend to be unstable. Without special care in their implementation, explicit extrapolation methods cause wavefield energy to grow exponentially with depth, contrary to physical expectations.
One recent technique, Hale-McClellan 3D Prestack Depth Migration (HM 3DPSDM) is an explicit extrapolation method applied to prestack data. The details of HM 3DPSDM is disclosed in publications: Hale, D., xe2x80x9cStable explicit depth extrapolation of seismic wavefields,xe2x80x9d Geophysics, Vol. 56 No. 11 (November 1991) p. 1770-1777; and Hale, D., xe2x80x9c3-D depth migration via McClellan transformations,xe2x80x9d Geophysics, Vol. 56 No. 11 (November 1991) p. 1778-1785, both of which are incorporated by reference. HM 3DPSDM has been proven to be a cost-effective wavefield imaging technique that has stirred up much hope in the oil industry to provide more accurate images of the subsurface. However, major sources of errors in extrapolation are depth-variable reference slowness and lateral slowness variation. Depth-variable reference slowness refers to the migration velocity having horizontal velocity variations. Lateral slowness variation refers to the migration velocity having lateral velocity variations. Typically, seismic data will contain both these variations and, hence, the process of extrapolation becomes quite complex.
Accordingly, an object of the present invention is to reduce the amount of noise in resolution images of seismic wave propagation caused by depth-variable reference slowness and lateral slowness variations.
A more specific object of the present invention is to provide a method of analyzing seismic data using HM 3DPSDM that enhances the imaging quality of the seismic data and reduce the requirement for small extrapolation depth steps.
A still further object of this invention is to produce a computer program which generates high resolution images of seismic wave propagation.
According to the present invention the foregoing and other objects are attained in a method for imaging a three-dimensional (3D) seismic data volume containing a plurality of data points having x, y and z coordinates defining a physical location in said seismic data volume, wherein said data points have an associated wave velocity. The method comprises downwardly extrapolating the data corresponding to a particular depth to obtain a desired physical quantity. A series of Li-correction operators is calculated for at least a portion of the depths. The Li-correction operators correspond to a series of reference velocities. Generally, the series of reference velocities are determined by selecting a minimum reference velocity and a maximum reference velocity and a step interval for increasing the reference velocity starting with the minimum reference velocity and continuing until the maximum reference velocity is reached. After the series of Li-correction operators are calculated for a particular depth, they are each applied to the corresponding physical quantity obtained for the same depth thereby obtaining a series of reference physical quantities. Interpolation is then used to obtain a corrected physical quantity by using the series of reference physical quantities, the series of reference velocities and the associated velocity. In a particularly preferred embodiment a series of tapering operators are also calculated for each of the reference velocities and the tapering operators are applied to physical quantities for the corresponding depth when the Li-correction operators are applied.
In another aspect of the invention, an apparatus comprises a computer programmed to carry out the afore described method.